Interaction of the vector-meson octet with the baryon octet in effective field theory

Abstract

We analyze the constraint structure of the interaction of vector mesons with baryons using the classical Dirac constraint analysis. We show that the standard interaction in terms of two independent SU(3) structures is consistent at the classical level. We then require the self-consistency condition of the interacting system in terms of perturbative renormalizability to obtain relations for the renormalized coupling constants at the one-loop level. As a result we find a universal interaction with one coupling constant which is the same as in the massive Yang-Mills Lagrangian of the vector-meson sector.

Light vector and axial mesons effective couplings to constituent quarks

“…The complete expressions for two of the form factors g r1 and g va−j , expressions (14) and (17), will be generalized for non zero momentum transfer. To explain the notation, two examples of full momentum dependent terms in expressions (13) and (15) are shown corresponding to a particular channel of the diagrams shown in Fig. 1.…”

“…The structureless mesons limit was considered for the zero order derivative and large quark effective mass expansion. The leading vector mesons-constituent quark interactions are the minimal gauge couplings in expression (13). The determinant expansion given by expression (10) can be written in terms of a covariant derivative for the minimal coupling with vector/axial mesons.…”

“…However these effective couplings do not represent all the possible effective couplings since tensor quark currents are not obtained from the method presented in this work. The resulting leading single meson couplings (13) are the only renormalizable effective couplings and the higher order ones, such as (15), are non renormalizable. All the coupling constants, however, are UV finite for usual large momentum behaviors of the gluon propagator such as D(p) ∼ 1/p s for s > 2.…”

Chiral constraints on the isoscalar electromagnetic spectral functions of the nucleon from leading order vector meson couplings

“…We take the couplings as G F = g and G D = 0 which results from the constraint analysis and the perturbative renormalizability condition on the vector meson octet and baryon octet interaction of Ref. [26]. The low-energy constants D and F can be determined by fitting to the semi-leptonic baryon decays at tree level.…”

Mass and width of theΔ(1232)resonance using complex-mass renormalization

“…Here, we make use of the constraint analysis of Ref. [55] using the canonical (Hamilton) formalism [56][57][58][59][60], which results in a self-consistent theory with the correct number of degrees of freedom and leads to consistent interactions of the Delta resonance with pions and nucleons. As a consequence of the constraint analysis, the Lagrangian is invariant under the so-called point transformation [55,61,63], and we may set the so-called off-shell parameter A to −1, which also results in a simplified form of the Delta propagator.…”